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LIX. Note on the Elasticity of Liquid Films and the 

 Foaming of Solutions. By S. A. Shokter, B.Sc, Assistant 

 Lecturer in Physics in the University of Leeds *. 



XN the July number of the Philosophical Magazine, 

 Prof. Pollock raises some interesting questions with 

 regard to the foaming of solutions. I have been engaged 

 for some time in theoretical and experimental investigations 

 relating to this subject, and perhaps a short preliminary 

 account of my theory of the elasticity of liquid films will 

 throw some light on these questions. 



According to Gibbs's theory of capillarity, a solute, the 

 further addition of which to the solution lowers the surface 

 tension, will be more concentrated in the surface layers than 

 in the body of the solution. Gibbs obtains an expression 

 for the " surface excess " which involves the chemical 

 potentials of the components of the solution. I have extended 

 Gibbs's theory and obtained expressions for the practical 

 calculation of the surface excess, applicable to solutions of 

 ;inv degree of concentration. This general theory is rather 

 complicated. The present discussion is limited to the case 

 of an ideal dilute solution. This limitation, while it sim- 

 plifies very considerably th ■■ mathematical treatment, does 

 not deprive the discussion of any of its physical essentials. 

 In the case of an ideal dilute solution, my theory leads to 

 Milner'sf well-known expression 



ne-dc' 



where V is the surface excess (per unit area of surface), 

 t the surface tension, the temperature, R the gas constant, 

 and c the concentration (in mass of solute per unit volume 

 of solution). 



The extension of a film of a pure liquid causes no increase 

 in the surface tension. Hence such a film can have only a 

 brief existence. Thus if different parts of the film are at 

 different levels, gravity will lead to an indefinite thinning of 

 the upper parts, and hence to the rupture of the film. The 

 case of a film of a solution, in which the solute has a marked 

 lowering effect on the surface tension, is quite different. If 

 such a film be extended, equilibrium between the surface 

 layers and the interior of the film is disturbed, and the 

 tension is increased. While this equilibrium is being re- 

 established the tension will decrease, but not to its original 



* Communicated bv the Author. 



t Phil. Mag. vol. xiii. p. 96, Jan. 1907. 



Phil. Mag. S. 6. Vol. 24. No. 142. Oct. 1912. 2 T 



